Abstract

Under study is some mathematical model of the radiation transfer process in a scattering medium initiated by a pulsed point isotropic source. We inspect the inverse problem of finding a diffusely reflecting curve by using the two integral overdetermination conditions on the solution of the radiative transfer equation. Some nonlinear differential equation is obtained for the function that describes the shape of the desired curve in the case of the single scattering approximation. Numerical analysis of the inverse problem solution is carried out to check the stability under perturbations of the initial data .

中文翻译：

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脉冲测深法在散射介质中朗伯曲线的重构

摘要

正在研究的是由脉冲点各向同性源引发的散射介质中辐射传输过程的一些数学模型。我们通过在辐射传递方程的解上使用两个积分超确定条件来检验找到漫反射曲线的反问题。对于该函数，获得了一些非线性微分方程，该方程描述了单次散射近似情况下所需曲线的形状。进行了反问题解的数值分析，以检验初始数据摄动下的稳定性。